The generator matrix

 1  0  0  0  1  1  1 3X+2  1 2X  1 3X 3X  1  1  1  1  X  1  X  1  X 2X+2  0  1  1  1 3X+2  1
 0  1  0  0  X 2X+1  1  1  2 X+2 X+3  1  1 3X+3  2  0  0  0 3X+2 3X 3X+3  1 2X  1 X+1 2X+3 X+3  0  0
 0  0  1  0 X+1  1  X X+1 X+1  1 2X+2  2  3  3  0 2X+2  3 3X 2X+3  1 3X+3 X+3  1 2X+2 3X+2 3X+1 2X+2  1  0
 0  0  0  1  1  2 X+3 X+1  X  3 X+2 X+1  X  3 X+3 3X  3  1  2 3X+1 X+1 X+2  0 X+2 2X+3 X+2  2 3X+1  0
 0  0  0  0  2 2X 2X+2  2  0  2  0 2X+2  2 2X 2X 2X+2  0  2 2X+2  0 2X+2  0 2X+2  2  2 2X+2 2X  0  0

generates a code of length 29 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+90x^22+700x^23+2496x^24+6464x^25+15904x^26+30340x^27+47336x^28+55280x^29+47234x^30+30900x^31+16103x^32+6192x^33+2182x^34+652x^35+208x^36+32x^37+28x^38+2x^42

The gray image is a code over GF(2) with n=232, k=18 and d=88.
This code was found by Heurico 1.16 in 194 seconds.